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Nathanson","submitted_at":"2005-03-09T15:21:42Z","abstract_excerpt":"For every positive integer $n$, the quantum integer $[n]_q$ is the polynomial $[n]_q = 1 + q + q^2 + ... + q^{n-1}.$ A quadratic addition rule for quantum integers consists of sequences of polynomials $\\mathcal{R}' = \\{r'_n(q)\\}_{n=1}^{\\infty}$, $\\mathcal{S}' = \\{s'_n(q)\\}_{n=1}^{\\infty}$, and $\\mathcal{T}' = \\{t'_{m,n}(q)\\}_{m,n=1}^{\\infty}$ such that $[m+n]_q = r'_n(q)[m]_q + s'_m(q)[n]_q + t'_{m,n}(q)[m]_q[n]_q$ for all $m$ and $n.$ This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials \\polf that satisfy the associated functional"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0503177","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-03-09T15:21:42Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"27fb876de6a02d07038344bbdce98ca8510502fdaefe639d3d77c77d23f3f22f","abstract_canon_sha256":"9d62ecb302534aa1aa680ee7bee05674abddbbba268ed94f9f63cc89d67ad9c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:45.961104Z","signature_b64":"+XQLaZRZFnb7F6Z6U9Ozm/i4woH6w0pf3Nkia6VqLVLYnhP1st+n5vsLKd9/UplCxwJ/jQywacL2vGrqaLGsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84cdac9e49e10801f761dc35dbd8f663c61a1632bc3524fa80e780d949011a63","last_reissued_at":"2026-05-18T00:53:45.960755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:45.960755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic addition rules for quantum integers","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.NT","authors_text":"Alex V. 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